Setup: We experiment with the distortion loss proposed in [1]} (formulas in Appendix REF ), which minimizes the relation between the distance in the space, compared to the distance in the graph, and captures the average distortion. As input and evaluation data we take the shortest distance in the graph between every pair of connected nodes. Unlike previous work [2]}, [1]} we do not apply any scaling, neither in the input graph distances nor in the distances calculated on the space.
Since the point \(\textbf {0}\)  is not part of the Siegel upper-half space, we initialize the matrix embeddings by adding small symmetric perturbations to the matrix basepoint \(i{\rm Id}\)  (see Appendix REF ). For the Bounded model, we additionally map the points with the Cayley transform. More experimental details in Appendix .
